Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 7.5   b = 6.2   c = 1.85

Area: T = 4.46768462291
Perimeter: p = 15.55
Semiperimeter: s = 7.775

Angle ∠ A = α = 128.842234364° = 128°50'32″ = 2.24987231125 rad
Angle ∠ B = β = 40.08109842677° = 40°4'52″ = 0.76995451429 rad
Angle ∠ C = γ = 11.07766720925° = 11°4'36″ = 0.19333243982 rad

Height: ha = 1.19111589944
Height: hb = 1.44109181384
Height: hc = 4.82990229504

Median: ma = 2.62108300212
Median: mb = 4.49773603369
Median: mc = 6.81883117412

Inradius: r = 0.57545139844
Circumradius: R = 4.81546385385

Vertex coordinates: A[1.85; 0] B[0; 0] C[5.73985135135; 4.82990229504]
Centroid: CG[2.53295045045; 1.61096743168]
Coordinates of the circumscribed circle: U[0.925; 4.72549464818]
Coordinates of the inscribed circle: I[1.575; 0.57545139844]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 51.15876563602° = 51°9'28″ = 2.24987231125 rad
∠ B' = β' = 139.9199015732° = 139°55'8″ = 0.76995451429 rad
∠ C' = γ' = 168.9233327907° = 168°55'24″ = 0.19333243982 rad

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How did we calculate this triangle?

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 7.5+6.2+1.85 = 15.55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 15.55 }{ 2 } = 7.78 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 7.78 * (7.78-7.5)(7.78-6.2)(7.78-1.85) } ; ; T = sqrt{ 19.95 } = 4.47 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4.47 }{ 7.5 } = 1.19 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4.47 }{ 6.2 } = 1.44 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4.47 }{ 1.85 } = 4.83 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos alpha ; ; alpha = arccos( fraction{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 6.2**2+1.85**2-7.5**2 }{ 2 * 6.2 * 1.85 } ) = 128° 50'32" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 7.5**2+1.85**2-6.2**2 }{ 2 * 7.5 * 1.85 } ) = 40° 4'52" ; ; gamma = 180° - alpha - beta = 180° - 128° 50'32" - 40° 4'52" = 11° 4'36" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4.47 }{ 7.78 } = 0.57 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 7.5 }{ 2 * sin 128° 50'32" } = 4.81 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.2**2+2 * 1.85**2 - 7.5**2 } }{ 2 } = 2.621 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.85**2+2 * 7.5**2 - 6.2**2 } }{ 2 } = 4.497 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.2**2+2 * 7.5**2 - 1.85**2 } }{ 2 } = 6.818 ; ;
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